Leaders go off and explore areas that show other people what is possible,вЂ™вЂќ Chuang said. ThatвЂ™s at least one reason why, when then-PhD student Lieven Vandersypen approached Chuang expressing an interest in leading an experiment, Chuang urged the young researcher to take on the first-ever realization of ShorвЂ™s algorithm on quantum hardware. First devised in 1994 by mathematician Peter Shor, the algorithm remains one of the most famous in all of quantum computing, and represents one of the starkest examples of theoretical quantum advantage.ДЇirst devised in 1994 by mathematician Peter Shor, the algorithm remains one of the most famous in all of quantum computing, and represents one of the starkest examples of theoretical quantum advantage. ShorвЂ™s factoring algorithm, however, does just that by leveraging the properties of quantum superposition and interference. Some classical algorithms can factor large integers in sub-exponential time, but theorists have yet to find a classical method that can get the job done in polynomial time. Exponential time is much slower than the algorithms used for common mathematical operations like addition, multiplication, or calculating square roots, which all have polynomial time complexity. This means classical factoring algorithms generally have exponential вЂњtime complexity,вЂќ which is the measure of how long it takes to run an algorithm relative to the length of its input. вЂњWe knew nobody else could do it,вЂќ Chuang said.ДЇor most classical factoring algorithms, the computational effort that goes into finding the factors of any given integer grows exponentially with the number of digits in the integer itself. Implementing ShorвЂ™s algorithm would be a formidable test of those capabilities. By 2001, Chuang and his colleagues were eager to вЂњshow offвЂќ what they could do using IBMвЂs engineering prowess and ability to perform experiments at scale. However, that system was incapable of solving meaningful problems. вЂњAll of the experiments people had been doing with quantum computation until that time were small scale,вЂќ Chuang said in a recent interview.Д¬huang, a former IBM researcher and leader of the 2001 experiment, had previously used NMR techniques to help develop one of the very first functional quantum computers in 1998. Quantum computing pioneer Isaac вЂњIkeвЂќ Chuang says that the 2001 factoring experiment was significantly more ambitious than similar efforts that preceded it.

Now, as we celebrate a major milestone in the history of quantum computing, letвЂ™s take a look back at this historic achievement and its impact on the broader quantum community. This helped kick off a boom in quantum hardware development that continues to this day. Their work was among the first to show that quantum computing was more than just an interesting thought experiment, and that researchers could exercise enough control over quantum systems to execute hundreds of complex operations and generate meaningful results. That experiment was conducted by researchers at IBM Research-Almaden in San Jose, CA, who used an early kind of quantum computer called a liquid state nuclear magnetic resonance quantum computer to successfully factor the number 15. Last month marked the 20th anniversary of the first published experimental realization of ShorвЂ™s algorithm, which appeared in the December 2001 issue 1 of Nature. Twenty years ago, a team of researchers became the first to demonstrate this algorithm on real quantum hardware, changing the field of quantum computing forever. Not only does this have potential impact for cryptography, but it could provide exciting advances in fields like machine learning. The inefficiency of classical factoring techniques also drives much of the excitement surrounding quantum computers, which might be able to factor large numbers much more efficiently using Peter ShorвЂ™s landmark algorithm. This simple truth forms the basis of many modern encryption algorithms, which use large numbers and their prime factors to secure data.

Classical factoring algorithms are generally quite computationally expensive, especially when it comes to factoring large integers.

Peter shor quantum error correction